reserve x,y,z,w for ExtReal,
  r for Real;
reserve f,g for ExtReal;
reserve t for ExtReal;

theorem Th66:
  x*(y*z) = (x*y)*z
proof
  per cases;
  suppose
    x is real & y is real & z is real;
    then reconsider r=x, s=y, t=z as Real;
    reconsider rs = r*s, sx = s*t as Real;
    thus x*(y*z) = r*sx .= rs*t
      .= (x*y)*z;
  end;
  suppose
    x is not real or z is not real;
    hence thesis by Lm22;
  end;
  suppose
    y is not real;
    hence thesis by Lm21;
  end;
end;
